Results 1 to 3 of 3

Math Help - Tetrahedron

  1. #1
    Senior Member
    Joined
    Jan 2009
    Posts
    381

    Tetrahedron

    In the tetrahedron ABCD , AB = BC =10 , AC=8\sqrt{2} , AD=CD=8 cm and BD = 6 cm . Show that the line from C perpendicular to AB and the line from D perpendicular to AB meet at a point AB .

    I can see from the sketch and deduce that they meet at the same point . But how can i show mathematically . THanks !!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by thereddevils View Post
    In the tetrahedron ABCD , AB = BC =10 , AC=8\sqrt{2} , AD=CD=8 cm and BD = 6 cm . Show that the line from C perpendicular to AB and the line from D perpendicular to AB meet at a point AB .

    I can see from the sketch and deduce that they meet at the same point . But how can i show mathematically . THanks !!
    1. Show that triangle ABD is a right triangle.

    2. Calculate DF (=4.8) (it's the height in the right triangle!)

    3. Calculate AF ( = 6.4) and BF (=3.6) (use Euclid's theorem)

    4. Calculate the length of CF in the right triangle AFC and calculate the length of CF in the right triangle BFC. In both cases you'll get the same result. Therefore the lines DF and CF are perpendicular on AB and meet in the same point.
    Attached Thumbnails Attached Thumbnails Tetrahedron-strck_im4flach.png  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466
    Quote Originally Posted by thereddevils View Post
    In the tetrahedron ABCD , AB = BC =10 , AC=8\sqrt{2} , AD=CD=8 cm and BD = 6 cm . Show that the line from C perpendicular to AB and the line from D perpendicular to AB meet at a point AB .

    I can see from the sketch and deduce that they meet at the same point . But how can i show mathematically . THanks !!
    They are in different planes. If they meet at all, it must be on line AB. Call the point at which the line from D meets AB, P. Then ADP is a right triangle with hypotenuse, AD, of length 8. The lengths of AP and DP are unknown. Call them x and y, respectively. We have x^2+ y^2= 64 Similarly BDP is a right triangle with hypotenuse, DB, of length 6. The lengths of BP is unknown. Call it z. Since DP is also a leg in this triangle, we must have y^2+ z^2= 36. We must also have x+ z= 10. That gives three equations to solve for x, y, and z.

    Do the same with the right triangles APC and BPC and show that x and z, the distances from A to P and from B to P are the same for both problems.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. tetrahedron,
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: July 14th 2009, 01:09 AM
  2. tetrahedron
    Posted in the Geometry Forum
    Replies: 1
    Last Post: January 8th 2009, 12:35 PM
  3. tetrahedron 2
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 29th 2008, 07:21 PM
  4. tetrahedron
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 29th 2008, 02:26 PM
  5. Tetrahedron
    Posted in the Geometry Forum
    Replies: 4
    Last Post: March 21st 2008, 01:07 AM

Search Tags


/mathhelpforum @mathhelpforum